1. 13
Exponents and Polynomials

2. 13.3 Multiplying Polynomials
Objectives
1. Multiply a monomial and a polynomial. 2. Multiply two polynomials. 3. Multiply binomials by the FOIL method.

3. Multiply a Monomial and a Polynomial
Example 1 Find each product.
(a) 5x ( 6x ) 2 4
= 5x ( 6x ) 2 4 +
5x ( 7 ) 2
Distributive property
= 30x x 6 2
Multiply monomials.

4. Multiply a Monomial and a Polynomial
Example 1 (concluded) Find each product.
(b) – 2h ( – 3h h – 1 ) 4 9 2
Distributive property
= – 2h (– 3h ) 4 9
+ (– 2h ) (8h ) 4 2
+ (– 2h )(– 1) 4
= 6h 13
– 16h 6
+ 2h 4
Multiply monomials.

5. Multiply Two Polynomials
Multiplying Polynomials
To multiply two polynomials, multiply each term of the
second polynomial by each term of the first polynomial
and add the products.

6. Multiply Two Polynomials
Example 2
( 2y – 5 ) ( 2y – 7y ) 2 3
Distributive property =
(2y ) 2 3
(–7y)
(2y ) 2 +
(4)
(2y ) 2 +
(–5)
(2y ) 3 +
(–7y) +
(–5)
(4) +
(–5) = 4y 5
14y 3 – 8y 2 + –
10y 3 +
35y
– 20 = 4y 5
24y 3 – 8y 2 +
35y
– 20
Combine like terms.

7. Multiply Two Polynomials
Example 3
5n n – 3n – 2 3 2 4n 2
15n 3
+ 24n 2
– 9n
– 6
20n 5
+ 32n 4
– 12n 3
– 8n 2
20n 5
+ 32n 4
+ 3n 3
+ 16n 2
– 9n
– 6

8. Multiply Binomials by the FOIL Method
Multiplying Binomials by the FOIL Method
Step 1 Multiply the two First terms of the binomials to get the first term of the answer.
Step 2 Find the Outer product and the Inner product and add them (when possible) to get the middle term of the answer.
Step 3 Multiply the two Last terms of the binomials to get the last term of the answer.

9. Multiply Binomials by the FOIL Method
Example 4 F O I L
= 3y – 2y – 12y + 8 2
( y – 4 ) ( 3y – 2 )
= 3y – 14y + 8 2
Multiply the first terms:
y ( 3y ) F
Multiply the outer terms:
y ( – 2 ) O
Multiply the inner terms:
– 4 ( 3y ) I
Multiply the last terms:
– 4 (– 2 ) L

10. Multiply Binomials by the FOIL Method
Example 5 F O I L
= 5n + n – 35n – 7 2
( n – 7 ) ( 5n )
= 5n – 34n – 7 2
Multiply the first terms:
n ( 5n ) F
Multiply the outer terms:
n ( 1 ) O
Multiply the inner terms:
– 7 ( 5n ) I
Multiply the last terms:
– 7 ( 1 ) L

11. Multiply Binomials by the FOIL Method
Example F O I L
= 27g – 12g + 18g – 8 2
( 3g ) ( 9g – 4 )
= 27g + 6g – 8 2
Multiply the first terms:
3g ( 9g ) F
Multiply the outer terms:
3g ( – 4 ) O
Multiply the inner terms:
2 ( 9g ) I
Multiply the last terms:
2 ( – 4 ) L

12. Multiply Binomials by the FOIL Method
Example 6 F O I L
= 24a – 12ab + 12ab – 6b 2
( 6a + 3b ) ( 4a – 2b )
= 24a – 6b 2
Multiply the first terms:
6a ( 4a ) F
Multiply the outer terms:
6a ( – 2b ) O
Multiply the inner terms:
3b ( 4a ) I
Multiply the last terms:
3b ( – 2b ) L